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- W2787380050 abstract "A series-parallel graph can be built from a single-edge graph by a sequence of series and parallel extensions. The class of such graphs coincides with the class of graphs that do not have the complete graph K4 as a minor. This dissertation considers a class M1 of graphs that are close to being series-parallel. In particular, every member of the class has the property that one can obtain a series-parallel graph by adding a new edge and contracting it out, or by splitting a vertex into two vertices whose neighbor sets partition the neighbor set of the original vertex. The class M1 is minor-closed. The goal of this dissertation is to show that M1 has exactly twelve excluded minors, including K5, the cube, and the octahedron." @default.
- W2787380050 created "2018-02-23" @default.
- W2787380050 creator A5015526012 @default.
- W2787380050 date "2022-06-10" @default.
- W2787380050 modified "2023-10-15" @default.
- W2787380050 title "Characterizations of Some Classes of Graphs That Are Nearly Series-Parallel" @default.
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- W2787380050 doi "https://doi.org/10.31390/gradschool_dissertations.4179" @default.
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